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Comments on Homeworks 1 and 2
Homework 1, Question 4.
I wasn’t as explicit as I could have been. Technically, you could just write
∀
x
(if
x
is real, then
e
x
is positive)
∀
x
(if
x
is an integer, then
x
can’t be both even and odd)
∀
x
(if
x
is a prime number, there is another prime number that’s bigger)
However, the sentences have more structure than that. What I had in mind
was to translate further into symbols. For instance,
∀
x
±
(
x
is real)
→
(
e
x
is positive)
²
∀
x
±
(
x
is an integer)
→ ¬
³
(
x
is even)
∧
(
x
is odd)
´
²
∀
x
±
(
x
is prime)
→ ∃
y
³
(
y
is prime)
∧
(
y
is greater than
x
)
´
²
You can translate even further into symbols than that. For instance, you
could make up symbols for predicates, such as
R
(
x
) = “
x
is real” (we could also write “
x
∈
R
”)
P
(
x
) = “
x
is positive” (we could also write “
x >
0”)
I
(
x
) = “
x
is an integer” (we could also write “
x
∈
Z
”)
E
(
x
) = “
x
is even”
O
(
x
) = “
x
is odd”
Q
(
x
) = “
x
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 Spring '08
 Staff

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